The harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs $(x,y)$ of positive integers is the harmonic mean of $x$ and $y$ equal to $20$

The exponent rules are given below.

We are given that;

To state exponent rules

Now,

Exponent rules are the laws or principles that govern the operations on numbers or variables with exponents. An exponent is a number or a variable that tells how many times to use the base in a multiplication.

There are different exponent rules for different situations, such as multiplying, dividing, raising to another power, or having a negative or fractional exponent. Here is a table of some common exponent rules with examples:

| Rule | Example |

[tex]| x^1 = x | 6^1 = 6 |[/tex]

[tex]| x^0 = 1 | 7^0 = 1 |[/tex]

[tex]| x^-1 = 1/x | 4^-1 = 1/4 |[/tex]

[tex]| x^m * x^n = x^(m+n) | 2^3 * 2^4 = 2^(3+4) = 2^7 |[/tex]

[tex]| x^m / x^n = x^(m-n) | 2^5 / 2^3 = 2^(5-3) = 2^2 |[/tex]

[tex]| (x^m)^n = x^(mn) | (2^3)^2 = 2^(3*2) = 2^6 |[/tex]

[tex]| (xy)^n = x^n * y^n | (3*4)^2 = 3^2 * 4^2 |[/tex]

[tex]| (x/y)^n = x^n / y^n | (4/2)^3 = 4^3 / 2^3 |[/tex]

[tex]| x^(m/n) = n-th root of x^m | 2^(6/3) = cube root of 2^6 |[/tex]

We can use these rules to simplify expressions with exponents or to perform calculations with them.

Therefore, by exponentiation answer will be given.

Learn more about exponentiation here:

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The complete question is;

List all the rules of exponentiation.

Answer:

5 and a half hours

Step-by-step explanation:

347.5-100=247.5

247.5/45=5.5

Answer:

Kaya rented the limo for about 5 and a half hours

                             Hope this helps! good luck :)

Answer:

13 hours

Step-by-step explanation:

to drive 567 miles in 9 hours you would be going 63mph and it would take 13 hours at 63 mph to travel 819 miles.

Answer: 90 degrees

Step-by-step explanation: ez

Answer:

are congruent

Step-by-step explanation:

If two polygons are congruent, then they have the same area.

Two polygons are congruent if their corresponding sides and angles are congruent. Note: Two sides are congruent if they have the same length and angles are congruent if they have the same measure. We indicate that angles are congruent by putting the same number of slash marks through each angle.

Answer:

Step-by-step explanation:

Given that

1gallon=3.8liters

0.5gallon=x

x=0.5*3.8

x=1.9liters

we know that 1liter is 1000cm^3

                       1.9liter is x

x=1900cm^3

Now we have the volume of water poured in cm^3

the volume of a rectangular prism is

volume=l*w*h

1900=30*20*h

1900=600h

h=1900/600

h= 3.16cm

Step-by-step explanation:

If the domain doesn't have 1 or 4 in it. This means 1 and 4 are the zeroes of the denomiator of the rational function.

So

[tex](x - 1)(x - 4)[/tex]

[tex]( {x}^{2} - 5x + 4)[/tex]

So that is the denomiator.

The numerator passes through (-3,3).

Let A represent a posible value of the numerator.

[tex]y = \frac{a}{( {x}^{2} - 5x + 4) } [/tex]

Plug in -3 for x and 3 for y.

[tex]3 = \frac{a}{ - 3 {}^{2} - 5( - 3) + 4 } [/tex]

[tex]3 = \frac{a}{9 + 15 + 4} [/tex]

[tex]3 = \frac{a}{28} [/tex]

[tex]84 = a[/tex]

So one possible function is

[tex]y = \frac{84}{ {x}^{2} - 5x + 4 } [/tex]

Answer:

area= 22cm× 14cm= 308cm²

please mark it as brainlist answer

Step-by-step explanation:

The area under the curve shaded is -1 to 2 is 13.59%.

The z score is a measure used in statistic to determine by how much standard deviations the raw score is above or below the mean.

If the raw score is greater than the mean then the z score is positive but if the raw score is less than the mean then the z score is negative.

The formula of z score

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]\mu=mean[/tex]

[tex]\sigma=standard deviation[/tex]

x=raw score

From the normal distribution table,

Area between z = -2 and z =-1  is given by

P(-2 < z < -1) implies that  P(z < -2) - P(z < -1) that is

 P(z < -2) - P(z < -1) = 0.1587 - 0.0228

P(z < -2) - P(z < -1) = 0.1359

P(z < -2) - P(z < -1) = 13.59%

Therefore we get the area under the curve shaded is -1 to 2 is 13.59%.

To learn more about the area under the curve visit:

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Answer:

μ = $240

σ = $50

Step-by-step explanation:

Profit is revenue minus cost:

P = R – C

The revenue is $2 times the number of slices sold, and the cost is $160.

P = 2x – 160

The average profit is:

μ = 2(200) – 160

μ = 240

The standard deviation is:

σ = 2(25)

σ = 50

Answer:

f=3

Step-by-step explanation:

4=2f-2

6=2f

f=3

Answer:

f=3

Step-by-step explanation:

Answer:

z= - 1/2h + 1/2b

Step-by-step explanation:

-2z + b = h

-2z = h - b

z= - 1/2h + 1/2b

Answer:

E, 3/2

Step-by-step explanation:

First, say that the numerator is 2^2001 * 3^2001 * 3^2, so that the powers will align. Then, we can combine 2^2001 and 3^2001 for 6^2001. If we ignore the 3^2, we get 6^2001/6^2002, which simplifies to 1/6. If we multiply 9 (which is 3^2) to 1/6, we get 9/6=3/2. This is a pretty tough question. Hopefully this helps!

Using proportions, it is found that it will take 75 loads to move all the gravel.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In one load, they mode 80 pounds. How many loads are needed to move 3 tons = 3 x 2000 = 6000 pounds? The rule of three is given as follows:

1 load - 80 pounds

x loads - 6000 pounds

Applying cross multiplication:

80x = 6000

x = 6000/80

x = 75.

It will take 75 loads to move all the gravel.

More can be learned about proportions at https://brainly.com/question/24372153

Answer: the greatist value is 30,000

Step-by-step explanation:

Answer:

Only one triangle is possible.

Step-by-step explanation:

Triangle inequality says that if sum of any two sides of the traingle is greater than the third side, then the triangle is possible.

Here,

,

Therefore, a triangle is possible with the given measurements,

Let us assume there is another triangle with same measurement with same measurements 7 cm, 6 cm, and 9 cm.,

By SSS congruency criteria both the triangles will be congruent.

Thus, all triangles with same measurement will be congruent to each other.

Hence, only one triangle is possible.

Answer:

25 is the geometric mean for two numbers

Step-by-step explanation:

Area of trapezium= 40cm²

½ h(b1+b2)=40

½ h (12+8)=40

½h (20)=40

h=40×2/20

h=4cm

we have to work money every day

Answer:

N 12

Step-by-step explanation:

Answer:

d=8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

16*9=144

144/6=24

24/3=8

d=8

Answer:

11 hours

Step-by-step explanation:

Answer:

9. Tan(57°)=~9.24 or 231/25

10. Sin(31°)= ~9.79 or ... 979/100

11. Sin(x°)= 15/23

12. Tan(x°)=37/8

Step-by-step explanation:

9. For the side length, we must use the given angle and the given side. We want to find the opposite given the adjacent side length of 6. We multiply tan(57°) by 6 using a scientific or graphing calculator and we get the answer  9.24 (after rounding) and then convert to a fraction in simplest form since it asked for a fraction. We would get 231/25

10. Just like the last question, we are given the opposite side length but not the hypotenuse. For this, we use sin. Multiply sin(31°) by 19 and we will getb 9.79 after rounding. Convert this into a fraction and we get 979/100 as the simplest form.

11. For this question we have 2 sides but not the angle. For this, we must use the SOH CAH TOA rule and just connect the pieces. We have the opposite and the hypotenuse or OH which means we have S which is sin. We then write Sin(x°)=15/23

12. For this we have the adjacent and opposite which is OA and that leaves us with T which is Tan(x°)=37/8. Remember that opposite comes before adjacent which is why it isn't 8/37. Hope this helps! (btw I'm not a bot)